Whisk barbecue sauce, water, tomato paste, molasses, salt and pepper in a medium bowl.
Heat oil in a large saucepan over medium heat. Add onion and collard greens and cook, stirring occasionally, until the collards are wilted, 3 to 5 minutes. Add sausage and cook, stirring, until beginning to brown, about 3 minutes more.
Reduce heat to medium-low; add beans and the sauce mixture to the pan. Gently stir to combine, cover and cook until heated through, about 3 minutes.